D-brane instantons and matrix models

TL;DR

This paper investigates whether the Dijkgraaf-Vafa matrix-model framework can perturbatively capture D-brane instanton effects in string compactifications, recasting stringy instantons as residual instantons of higgsed supergroups. By analyzing the planar limit and glueball dynamics for simple setups like the conifold and a $\mathbb{Z}_n$ orbifold quiver, it demonstrates exact agreement between matrix-model results and D-brane instanton calculations in the one-instanton sector, including how the leading stringy contributions arise from the matrix-model free energy via $W_{ ext{eff}}$. The work provides a practical perturbative route to compute stringy multi-instanton effects and offers a unified interpretation of exotic instantons within the DV/matrix-model paradigm. It also outlines future directions, such as extending to higher instanton orders, non-planar corrections, and connections to geometric transitions and topological string theory, with potential implications for broader classes of Calabi–Yau geometries and quiver theories.

Abstract

We point out that in some situations it is possible to use matrix model techniques a la Dijkgraaf-Vafa to perturbatively compute D-brane instanton effects. This provides an explanation in terms of stringy instantons of the results in hep-th/0311181. We check this proposal in some simple scenarios. We point out some interesting consequences of this observation, such as the fact that it gives a perturbative way of computing stringy multi-instanton effects. It also provides a further interpretation of D-brane instantons as residual instantons of higgsed supergroups.